Yes it will work with a single channel amp. The port can be used when powering it. I have a 2ch amp powering two subs, and I have it twisted in with the coupler on the sub.
And as for the LED strip, I am not to positive, I think it would be blown as most factory made are for 12v power source max. As the subs have varying (usually between 1-27v), it would most likely blow out the LEDs. Give it a try though! Take a look at the packaging and see what it says.